Equivalence and Accuracy Evaluation of Linearised State-Space Models of the Modular Multilevel Converter for Small-Signal Stability Analysis

This paper carries out a comparative assessment of two state-of-the-art linearised state-space models of the modular multilevel converter (MMC) to be used in system-level small-signal stability studies. The analysis focuses on the methods and assumptions that enable a linear time-invariant (LTI) representation of the MMC dynamics, which is characterized by multifrequency periodicity. The derivations of both models are briefly explained, focusing on the impact of the assumptions that enable an LTI representation. The equivalence of the models is assessed in time and frequency domains by carrying out small-signal step tests and calculating the eigenvalues of the converter, respectively. Both models are benchmarked in time domain against an averaged model of the MMC in PSCAD to evaluate their accuracies. The comparison of the two models demonstrates their equivalence and accuracies, and serves as a guideline in the selection of an appropriate state-space model of the MMC in system studies.